Karen Tripoli, K-5 Mathematics Department Head

tripoli@sch.ci.lexington.ma.us

**June 2016 – Article #7**

The eight *Standards for Mathematical Practice* in the Common Core and the *2011 Massachusetts State Framework for Mathematics* represent what mathematically proficient students are doing as they learn mathematics. This month, the last two *Practices* are illuminated.

Standard for Mathematical Practice #7

Look for and make use of structure

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well-remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property…. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects…-CCSS

You can help your child develop and apply this practice by encouraging him/her to persevere in order to reach a solution. Ask questions such as:

- What do you notice about the answers to the problems you just completed?
- What are some problems that are similar to this one?
- What patterns do you find in…?

Standard for Mathematical Practice #8

Look for and express regularity in repeated reasoning

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal… As they work to solve a problem, mathematically proficient students maintain oversight of the process while attending to the details. They continually evaluate the reasonableness of their intermediate results.

-CCSS

Ask questions such as:

- Can you think of a shortcut that will always work for problems like these?
- What pattern do you see? Can you make a rule or generalization?

April 2016 – Article #6

The eight *Standards for Mathematical Practice* in the Common Core and the *2011 Massachusetts State Framework for Mathematics* represent what mathematically proficient students are doing as they learn mathematics. Each month, one of the *Practices* is illuminated.

**Mathematics Practice Standard #6**

**Attend to Precision**

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently…. In the elementary grades, students give carefully formulated explanations to each other…

-CCSS

You can help your child develop and apply this practice by encouraging him/her to persevere in order to reach a solution. Ask questions such as:

- What do the symbols that you used mean?
- What units of measure are you using?
- Explain ________ (term used in a problem) to me.
- How did you know that your solution was reasonable?
- What symbols or notations are important in this problem?
- Does your solution answer the problem?
- Is there a more efficient strategy?

March 2016 – Article #5

The eight *Standards for Mathematical Practice* in the Common Core and the *2011 Massachusetts State Framework for Mathematics* represent what mathematically proficient students are doing as they learn mathematics. This month, two of the practices are illuminated.

Standard for Mathematical Practice #4

Model with mathematics

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life…. In early grades, this might be as simple as writing an addition equation to describe a situation…. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation…. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs… They… reflect on whether the results make sense.

-CCSS

You can help your child develop and apply this practice by encouraging him/her to persevere in order to reach a solution. Ask questions such as:

- Would it help to create a diagram, graph, table, etc.?
- What are some ways to visually represent the quantities?
- What number model could you construct to represent the problem?
- What is an equation or expression that matches the diagram? Number line? Chart? Table?

Standard for Mathematical Practice #5

Use appropriate tools strategically

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet… Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.

-CCSS

Ask questions such as:

- What mathematical tools could you use to visualize and represent the situation?
- What information do you have?
- In this situation, would it be helpful to use a graph? Number line? Ruler? Calculator?
- What approach are you considering trying first